Changeset a66b004 in sasmodels for doc


Ignore:
Timestamp:
Nov 30, 2017 12:30:08 AM (6 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
34bbb9c
Parents:
26a6608 (diff), b669b49 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.
Message:

Merge branch 'master' into boltzmann

Location:
doc
Files:
5 added
8 edited

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Unmodified
Added
Removed

  • doc/_extensions/dollarmath.py

    r103ea45 rdd4d95d  
    1212import re 
    1313 
    14 _dollar = re.compile(r"(?:^|(?<=\s|[(]))[$]([^\n]*?)(?<![\\])[$](?:$|(?=\s|[.,;)\\]))") 
     14_dollar = re.compile(r"(?:^|(?<=\s|[-(]))[$]([^\n]*?)(?<![\\])[$](?:$|(?=\s|[-.,;:?\\)]))") 
    1515_notdollar = re.compile(r"\\[$]") 
    1616 

  • doc/developer/calculator.rst

    r870a2f4 r2c108a3  
    77 
    88This document describes the layer between the form factor kernels and the 
    9 model calculator which implements the polydispersity and magnetic SLD 
     9model calculator which implements the dispersity and magnetic SLD 
    1010calculations.  There are three separate implementations of this layer, 
    1111:mod:`kernelcl` for OpenCL, which operates on a single Q value at a time, 
    … …  
    1414 
    1515Each implementation provides three different calls *Iq*, *Iqxy* and *Imagnetic* 
    16 for 1-D, 2-D and 2-D magnetic kernels respectively. 
    17  
    18 The C code is defined in *kernel_iq.c* and *kernel_iq.cl* for DLL and OpenCL 
    19 respectively.  The kernel call looks as follows:: 
     16for 1-D, 2-D and 2-D magnetic kernels respectively. The C code is defined 
     17in *kernel_iq.c*, with the minor differences between OpenCL and DLL handled 
     18by #ifdef statements. 
     19 
     20The kernel call looks as follows:: 
    2021 
    2122  kernel void KERNEL_NAME( 
    2223      int nq,                  // Number of q values in the q vector 
    23       int pd_start,            // Starting position in the polydispersity loop 
    24       int pd_stop,             // Ending position in the polydispersity loop 
    25       ProblemDetails *details, // Polydispersity info 
     24      int pd_start,            // Starting position in the dispersity loop 
     25      int pd_stop,             // Ending position in the dispersity loop 
     26      ProblemDetails *details, // dispersity info 
    2627      double *values,          // Value and weights vector 
    2728      double *q,               // q or (qx,qy) vector 
    2829      double *result,          // returned I(q), with result[nq] = pd_weight 
    29       double cutoff)           // polydispersity weight cutoff 
     30      double cutoff)           // dispersity weight cutoff 
    3031 
    3132The details for OpenCL and the python loop are slightly different, but these 
    … …  
    3435*nq* indicates the number of q values that will be calculated. 
    3536 
    36 The *pd_start* and *pd_stop* parameters set the range of the polydispersity 
    37 loop to compute for the current kernel call.   Give a polydispersity 
     37The *pd_start* and *pd_stop* parameters set the range of the dispersity 
     38loop to compute for the current kernel call.   Give a dispersity 
    3839calculation with 30 weights for length and 30 weights for radius for example, 
    3940there are a total of 900 calls to the form factor required to compute the 
    … …  
    4243the length index to 3 and the radius index to 10 for a position of 3*30+10=100, 
    4344and could then proceed to position 200.  This allows us to interrupt the 
    44 calculation in the middle of a long polydispersity loop without having to 
     45calculation in the middle of a long dispersity loop without having to 
    4546do special tricks with the C code.  More importantly, it stops the OpenCL 
    4647kernel in a reasonable time; because the GPU is used by the operating 
    … …  
    4950 
    5051The *ProblemDetails* structure is a direct map of the 
    51 :class:`details.CallDetails` buffer.  This indicates which parameters are 
    52 polydisperse, and where in the values vector the values and weights can be 
    53 found.  For each polydisperse parameter there is a parameter id, the length 
    54 of the polydispersity loop for that parameter, the offset of the parameter 
     52:class:`details.CallDetails` buffer.  This indicates which parameters have 
     53dispersity, and where in the values vector the values and weights can be 
     54found.  For each parameter with dispersity there is a parameter id, the length 
     55of the dispersity loop for that parameter, the offset of the parameter 
    5556values in the pd value and pd weight vectors and the 'stride' from one index 
    5657to the next, which is used to translate between the position in the 
    57 polydispersity loop and the particular parameter indices.  The *num_eval* 
    58 field is the total size of the polydispersity loop.  *num_weights* is the 
     58dispersity loop and the particular parameter indices.  The *num_eval* 
     59field is the total size of the dispersity loop.  *num_weights* is the 
    5960number of elements in the pd value and pd weight vectors.  *num_active* is 
    60 the number of non-trivial pd loops (polydisperse parameters should be ordered 
    61 by decreasing pd vector length, with a length of 1 meaning no polydispersity). 
     61the number of non-trivial pd loops (parameters with dispersity should be ordered 
     62by decreasing pd vector length, with a length of 1 meaning no dispersity). 
    6263Oriented objects in 2-D need a cos(theta) spherical correction on the angular 
    6364variation in order to preserve the 'surface area' of the weight distribution. 
    … …  
    7273*(Mx, My, Mz)*.  Sample magnetization is translated from *(M, theta, phi)* 
    7374to *(Mx, My, Mz)* before the kernel is called.   After the fixed values comes 
    74 the pd value vector, with the polydispersity values for each parameter 
     75the pd value vector, with the dispersity values for each parameter 
    7576stacked one after the other.  The order isn't important since the location 
    7677for each parameter is stored in the *pd_offset* field of the *ProblemDetails* 
    … …  
    7879values, the pd weight vector is stored, with the same configuration as the 
    7980pd value vector.  Note that the pd vectors can contain values that are not 
    80 in the polydispersity loop; this is used by :class:`mixture.MixtureKernel` 
     81in the dispersity loop; this is used by :class:`mixture.MixtureKernel` 
    8182to make it easier to call the various component kernels. 
    8283 
    … …  
    8788 
    8889The *results* vector contains one slot for each of the *nq* values, plus 
    89 one extra slot at the end for the current polydisperse normalization.  This 
    90 is required when the polydispersity loop is broken across several kernel 
    91 calls. 
     90one extra slot at the end for the weight normalization accumulated across 
     91all points in the dispersity mesh.  This is required when the dispersity 
     92loop is broken across several kernel calls. 
    9293 
    9394*cutoff* is a importance cutoff so that points which contribute negligibly 
    … …  
    9798 
    9899- USE_OPENCL is defined if running in opencl 
    99 - MAX_PD is the maximum depth of the polydispersity loop [model specific] 
     100- MAX_PD is the maximum depth of the dispersity loop [model specific] 
    100101- NUM_PARS is the number of parameter values in the kernel.  This may be 
    101102  more than the number of parameters if some of the parameters are vector 
    102103  values. 
    103104- NUM_VALUES is the number of fixed values, which defines the offset in the 
    104   value list to the polydisperse value and weight vectors. 
     105  value list to the dispersity value and weight vectors. 
    105106- NUM_MAGNETIC is the number of magnetic SLDs 
    106107- MAGNETIC_PARS is a comma separated list of the magnetic SLDs, indicating 
    107108  their locations in the values vector. 
    108 - MAGNETIC_PAR0 to MAGNETIC_PAR2 are the first three magnetic parameter ids 
    109   so we can hard code the setting of magnetic values if there are only a 
    110   few of them. 
    111109- KERNEL_NAME is the name of the function being declared 
    112110- PARAMETER_TABLE is the declaration of the parameters to the kernel: 
    … …  
    152150    Cylinder2D:: 
    153151 
    154         #define CALL_IQ(q, i, var) Iqxy(q[2*i], q[2*i+1], \ 
     152        #define CALL_IQ(q, i, var) Iqxy(qa, qc, \ 
    155153        var.length, \ 
    156154        var.radius, \ 
    157155        var.sld, \ 
    158         var.sld_solvent, \ 
    159         var.theta, \ 
    160         var.phi) 
     156        var.sld_solvent) 
    161157 
    162158- CALL_VOLUME(var) is similar, but for calling the form volume:: 
    … …  
    182178        #define INVALID(var) constrained(var.p1, var.p2, var.p3) 
    183179 
    184 Our design supports a limited number of polydispersity loops, wherein 
    185 we need to cycle through the values of the polydispersity, calculate 
     180Our design supports a limited number of dispersity loops, wherein 
     181we need to cycle through the values of the dispersity, calculate 
    186182the I(q, p) for each combination of parameters, and perform a normalized 
    187183weighted sum across all the weights.  Parameters may be passed to the 
    188 underlying calculation engine as scalars or vectors, but the polydispersity 
     184underlying calculation engine as scalars or vectors, but the dispersity 
    189185calculator treats the parameter set as one long vector. 
    190186 
    191 Let's assume we have 8 parameters in the model, with two polydisperse.  Since 
    192 this is a 1-D model the orientation parameters won't be used:: 
     187Let's assume we have 8 parameters in the model, two of which allow dispersity. 
     188Since this is a 1-D model the orientation parameters won't be used:: 
    193189 
    194190    0: scale        {scl = constant} 
    … …  
    196192    2: radius       {r = vector of 10pts} 
    197193    3: length       {l = vector of 30pts} 
    198     4: sld          {s = constant/(radius**2*length)} 
     194    4: sld          {s1 = constant/(radius**2*length)} 
    199195    5: sld_solvent  {s2 = constant} 
    200196    6: theta        {not used} 
    … …  
    202198 
    203199This generates the following call to the kernel.  Note that parameters 4 and 
    204 5 are treated as polydisperse even though they are not --- this is because 
     2005 are treated as having dispersity even though they don't --- this is because 
    205201it is harmless to do so and simplifies the looping code:: 
    206202 
    … …  
    210206    NUM_MAGNETIC = 2      // two parameters might be magnetic 
    211207    MAGNETIC_PARS = 4, 5  // they are sld and sld_solvent 
    212     MAGNETIC_PAR0 = 4     // sld index 
    213     MAGNETIC_PAR1 = 5     // solvent index 
    214208 
    215209    details { 
    … …  
    218212        pd_offset = {10, 0, 31, 32}   // *length* starts at index 10 in weights 
    219213        pd_stride = {1, 30, 300, 300} // cumulative product of pd length 
    220         num_eval = 300   // 300 values in the polydispersity loop 
     214        num_eval = 300   // 300 values in the dispersity loop 
    221215        num_weights = 42 // 42 values in the pd vector 
    222216        num_active = 2   // only the first two pd are active 
    … …  
    225219 
    226220    values = { scl, bkg,                                  // universal 
    227                r, l, s, s2, theta, phi,                   // kernel pars 
     221               r, l, s1, s2, theta, phi,                  // kernel pars 
    228222               in spin, out spin, spin angle,             // applied magnetism 
    229                mx s, my s, mz s, mx s2, my s2, mz s2,     // magnetic slds 
     223               mx s1, my s1, mz s1, mx s2, my s2, mz s2,  // magnetic slds 
    230224               r0, .., r9, l0, .., l29, s, s2,            // pd values 
    231225               r0, .., r9, l0, .., l29, s, s2}            // pd weights 
    … …  
    235229    result = {r1, ..., r130, pd_norm, x } 
    236230 
    237 The polydisperse parameters are stored in as an array of parameter 
    238 indices, one for each polydisperse parameter, stored in pd_par[n]. 
    239 Non-polydisperse parameters do not appear in this array. Each polydisperse 
     231The dispersity parameters are stored in as an array of parameter 
     232indices, one for each parameter, stored in pd_par[n]. Parameters which do 
     233not support dispersity do not appear in this array. Each dispersity 
    240234parameter has a weight vector whose length is stored in pd_length[n]. 
    241235The weights are stored in a contiguous vector of weights for all 
    … …  
    243237in pd_offset[n].  The values corresponding to the weights are stored 
    244238together in a separate weights[] vector, with offset stored in 
    245 par_offset[pd_par[n]]. Polydisperse parameters should be stored in 
     239par_offset[pd_par[n]]. Dispersity parameters should be stored in 
    246240decreasing order of length for highest efficiency. 
    247241 
    248 We limit the number of polydisperse dimensions to MAX_PD (currently 4), 
    249 though some models may have fewer if they have fewer polydisperse 
     242We limit the number of dispersity dimensions to MAX_PD (currently 4), 
     243though some models may have fewer if they have fewer dispersity 
    250244parameters.  The main reason for the limit is to reduce code size. 
    251 Each additional polydisperse parameter requires a separate polydispersity 
    252 loop.  If more than 4 levels of polydispersity are needed, then kernel_iq.c 
    253 and kernel_iq.cl will need to be extended. 
     245Each additional dispersity parameter requires a separate dispersity 
     246loop.  If more than 4 levels of dispersity are needed, then we need to 
     247switch to a monte carlo importance sampling algorithm with better 
     248performance for high-dimensional integrals. 
    254249 
    255250Constraints between parameters are not supported.  Instead users will 
    … …  
    262257theta since the polar coordinates normalization is tied to this parameter. 
    263258 
    264 If there is no polydispersity we pretend that it is polydisperisty with one 
    265 parameter, pd_start=0 and pd_stop=1.  We may or may not short circuit the 
    266 calculation in this case, depending on how much time it saves. 
     259If there is no dispersity we pretend that we have a disperisty mesh over 
     260a single parameter with a single point in the distribution, giving 
     261pd_start=0 and pd_stop=1. 
    267262 
    268263The problem details structure could be allocated and sent in as an integer 
    269264array using the read-only flag.  This would allow us to copy it once per fit 
    270265along with the weights vector, since features such as the number of 
    271 polydisperity elements per pd parameter or the coordinated won't change 
    272 between function evaluations.  A new parameter vector must be sent for 
    273 each I(q) evaluation.  This is not currently implemented, and would require 
    274 some resturcturing of the :class:`sasview_model.SasviewModel` interface. 
    275  
    276 The results array will be initialized to zero for polydispersity loop 
     266disperity points per pd parameter won't change between function evaluations. 
     267A new parameter vector must be sent for each I(q) evaluation.  This is 
     268not currently implemented, and would require some resturcturing of 
     269the :class:`sasview_model.SasviewModel` interface. 
     270 
     271The results array will be initialized to zero for dispersity loop 
    277272entry zero, and preserved between calls to [start, stop] so that the 
    278273results accumulate by the time the loop has completed.  Background and 
    … …  
    295290 
    296291This will require accumulated error for each I(q) value to be preserved 
    297 between kernel calls to implement this fully.  The kernel_iq.c code, which 
    298 loops over q for each parameter set in the polydispersity loop, will need 
    299 also need the accumalation vector. 
     292between kernel calls to implement this fully.  The *kernel_iq.c* code, which 
     293loops over q for each parameter set in the dispersity loop, will also need 
     294the accumulation vector. 

  • doc/developer/overview.rst

    r870a2f4 r3d40839  
    166166:ref:`Calculator_Interface` 
    167167 
     168.. _orientation_developer: 
     169 
     170Orientation and Numerical Integration 
     171------------------------------------- 
     172 
     173For 2d data from oriented anisotropic particles, the mean particle 
     174orientation is defined by angles $\theta$, $\phi$ and $\Psi$, which are not 
     175in general the same as similarly named angles in many form factors. The 
     176wikipedia page on Euler angles (https://en.wikipedia.org/wiki/Euler_angles) 
     177lists the different conventions available. To quote: "Different authors may 
     178use different sets of rotation axes to define Euler angles, or different 
     179names for the same angles. Therefore, any discussion employing Euler angles 
     180should always be preceded by their definition." 
     181 
     182We are using the $z$-$y$-$z$ convention with extrinsic rotations 
     183$\Psi$-$\theta$-$\phi$ for the particle orientation and $x$-$y$-$z$ 
     184convention with extrinsic rotations $\Psi$-$\theta$-$\phi$ for jitter, with 
     185jitter applied before particle orientation. 
     186 
     187For numerical integration within form factors etc. sasmodels is mostly using 
     188Gaussian quadrature with 20, 76 or 150 points depending on the model. It also 
     189makes use of symmetries such as calculating only over one quadrant rather 
     190than the whole sphere. There is often a U-substitution replacing $\theta$ 
     191with $cos(\theta)$ which changes the limits of integration from 0 to $\pi/2$ 
     192to 0 to 1 and also conveniently absorbs the $sin(\theta)$ scale factor in the 
     193integration. This can cause confusion if checking equations to include in a 
     194paper or thesis! Most models use the same core kernel code expressed in terms 
     195of the rotated view ($q_a$, $q_b$, $q_c$) for both the 1D and the 2D models, 
     196but there are also historical quirks such as the parallelepiped model, which 
     197has a useless transformation representing $j_0(a q_a)$ as $j_0(b q_a a/b)$. 
     198 
     199Useful testing routines include: 
     200 
     201:mod:`asymint` a direct implementation of the surface integral for certain 
     202models to get a more trusted value for the 1D integral using a 
     203reimplementation of the 2D kernel in python and mpmath (which computes math 
     204functions to arbitrary precision). It uses $\theta$ ranging from 0 to $\pi$ 
     205and $\phi$ ranging from 0 to $2\pi$. It perhaps would benefit from including 
     206the U-substitution for $\theta$. 
     207 
     208:mod:`check1d` uses sasmodels 1D integration and compares that with a 
     209rectangle distribution in $\theta$ and $\phi$, with $\theta$ limits set to 
     210$\pm 90/\sqrt(3)$ and $\phi$ limits set to $\pm 180/\sqrt(3)$ [The rectangle 
     211weight function uses the fact that the distribution width column is labelled 
     212sigma to decide that the 1-$\sigma$ width of a rectangular distribution needs to 
     213be multiplied by $\sqrt(3)$ to get the corresponding gaussian equivalent, or 
     214similar reasoning.] This should rotate the sample through the entire 
     215$\theta$-$\phi$ surface according to the pattern that you see in jitter.py when 
     216you modify it to use 'rectangle' rather than 'gaussian' for its distribution 
     217without changing the viewing angle. In order to match the 1-D pattern for 
     218an arbitrary viewing angle on triaxial shapes, we need to integrate 
     219over $\theta$, $\phi$ and $\Psi$. 
     220 
     221When computing the dispersity integral, weights are scaled by 
     222$|\cos(\delta \theta)|$ to account for the points in $\phi$ getting closer 
     223together as $\delta \theta$ increases. 
     224[This will probably change so that instead of adjusting the weights, we will 
     225adjust $\delta\theta$-$\delta\phi$ mesh so that the point density in 
     226$\delta\phi$ is lower at larger $\delta\theta$. The flag USE_SCALED_PHI in 
     227*kernel_iq.c* selects an alternative algorithm.] 
     228 
     229The integrated dispersion is computed at a set of $(qx, qy)$ points $(q 
     230\cos(\alpha), q \sin(\alpha))$ at some angle $\alpha$ (currently angle=0) for 
     231each $q$ used in the 1-D integration. The individual $q$ points should be 
     232equivalent to asymint rect-n when the viewing angle is set to 
     233$(\theta,\phi,\Psi) = (90, 0, 0)$. Such tests can help to validate that 2d 
     234models are consistent with 1d models. 
     235 
     236:mod:`sascomp -sphere=n` uses the same rectangular distribution as check1d to 
     237compute the pattern of the $q_x$-$q_y$ grid. 
     238 
     239The :mod:`sascomp` utility can be used for 2d as well as 1d calculations to 
     240compare results for two sets of parameters or processor types, for example 
     241these two oriented cylinders here should be equivalent. 
     242 
     243:mod:`\./sascomp -2d cylinder theta=0 phi=0,90 theta_pd_type=rectangle phi_pd_type=rectangle phi_pd=10,1 theta_pd=1,10 length=500 radius=10` 
     244 
    168245 
    169246Testing 

  • doc/genapi.py

    r2e66ef5 r706f466  
    5959    #('alignment', 'GPU data alignment [unused]'), 
    6060    ('bumps_model', 'Bumps interface'), 
     61    ('compare', 'Compare models on different compute engines'), 
    6162    ('compare_many', 'Batch compare models on different compute engines'), 
    62     ('compare', 'Compare models on different compute engines'), 
     63    ('conversion_table', 'Model conversion table'), 
    6364    ('convert', 'Sasview to sasmodel converter'), 
    6465    ('core', 'Model access'), 
    … …  
    8283    ('sasview_model', 'Sasview interface'), 
    8384    ('sesans', 'SESANS calculation routines'), 
     85    ('special', 'Special functions library'), 
    8486    ('weights', 'Distribution functions'), 
    8587] 

  • doc/guide/index.rst

    rc0d7ab3 rda5536f  
    1313   resolution.rst 
    1414   magnetism/magnetism.rst 
     15   orientation/orientation.rst 
    1516   sesans/sans_to_sesans.rst 
    1617   sesans/sesans_fitting.rst 

  • doc/guide/magnetism/magnetism.rst

    r1f058ea r4f5afc9  
    55 
    66Models which define a scattering length density parameter can be evaluated 
    7  as magnetic models. In general, the scattering length density (SLD = 
    8  $\beta$) in each region where the SLD is uniform, is a combination of the 
    9  nuclear and magnetic SLDs and, for polarised neutrons, also depends on the 
    10  spin states of the neutrons. 
     7as magnetic models. In general, the scattering length density (SLD = 
     8$\beta$) in each region where the SLD is uniform, is a combination of the 
     9nuclear and magnetic SLDs and, for polarised neutrons, also depends on the 
     10spin states of the neutrons. 
    1111 
    1212For magnetic scattering, only the magnetization component $\mathbf{M_\perp}$ 
    1313perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic 
    1414scattering length. 
    15  
    1615 
    1716.. figure:: 
    … …  
    2827is the Pauli spin. 
    2928 
    30 Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-) 
    31 to the $x'$ axis, the possible spin states after the sample are then 
     29Assuming that incident neutrons are polarized parallel $(+)$ and anti-parallel 
     30$(-)$ to the $x'$ axis, the possible spin states after the sample are then: 
    3231 
    33 No spin-flips (+ +) and (- -) 
     32* Non spin-flip $(+ +)$ and $(- -)$ 
    3433 
    35 Spin-flips    (+ -) and (- +) 
     34* Spin-flip $(+ -)$ and $(- +)$ 
     35 
     36Each measurement is an incoherent mixture of these spin states based on the 
     37fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample, 
     38with weighting: 
     39 
     40.. math:: 
     41    -- &= ((1-u_i)(1-u_f))^{1/4} \\ 
     42    -+ &= ((1-u_i)(u_f))^{1/4} \\ 
     43    +- &= ((u_i)(1-u_f))^{1/4} \\ 
     44    ++ &= ((u_i)(u_f))^{1/4} 
     45 
     46Ideally the experiment would measure the pure spin states independently and 
     47perform a simultaneous analysis of the four states, tying all the model 
     48parameters together except $u_i$ and $u_f$. 
    3649 
    3750.. figure:: 
    … …  
    4154$\phi$ and $\theta_{up}$, respectively, then, depending on the spin state of the 
    4255neutrons, the scattering length densities, including the nuclear scattering 
    43 length density ($\beta{_N}$) are 
     56length density $(\beta{_N})$ are 
    4457 
    4558.. math:: 
    4659    \beta_{\pm\pm} =  \beta_N \mp D_M M_{\perp x'} 
    47     \text{ when there are no spin-flips} 
     60    \text{ for non spin-flip states} 
    4861 
    4962and 
    … …  
    5164.. math:: 
    5265    \beta_{\pm\mp} =  -D_M (M_{\perp y'} \pm iM_{\perp z'}) 
    53     \text{ when there are} 
     66    \text{ for spin-flip states} 
    5467 
    5568where 
    5669 
    5770.. math:: 
    58     M_{\perp x'} = M_{0q_x}\cos(\theta_{up})+M_{0q_y}\sin(\theta_{up}) \\ 
    59     M_{\perp y'} = M_{0q_y}\cos(\theta_{up})-M_{0q_x}\sin(\theta_{up}) \\ 
    60     M_{\perp z'} = M_{0z} \\ 
    61     M_{0q_x} = (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\ 
    62     M_{0q_y} = (M_{0y}\sin\phi - M_{0x}\cos\phi)\sin\phi 
     71    M_{\perp x'} &= M_{0q_x}\cos(\theta_{up})+M_{0q_y}\sin(\theta_{up}) \\ 
     72    M_{\perp y'} &= M_{0q_y}\cos(\theta_{up})-M_{0q_x}\sin(\theta_{up}) \\ 
     73    M_{\perp z'} &= M_{0z} \\ 
     74    M_{0q_x} &= (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\ 
     75    M_{0q_y} &= (M_{0y}\sin\phi - M_{0x}\cos\phi)\sin\phi 
    6376 
    6477Here, $M_{0x}$, $M_{0x}$, $M_{0z}$ are the x, y and z components 
    … …  
    6679 
    6780.. math:: 
    68     M_{0x} = M_0\cos\theta_M\cos\phi_M \\ 
    69     M_{0y} = M_0\sin\theta_M \\ 
    70     M_{0z} = -M_0\cos\theta_M\sin\phi_M 
     81    M_{0x} &= M_0\cos\theta_M\cos\phi_M \\ 
     82    M_{0y} &= M_0\sin\theta_M \\ 
     83    M_{0z} &= -M_0\cos\theta_M\sin\phi_M 
    7184 
    7285and the magnetization angles $\theta_M$ and $\phi_M$ are defined in 
    … …  
    7689 
    7790===========   ================================================================ 
    78  M0_sld        = $D_M M_0$ 
    79  Up_theta      = $\theta_\mathrm{up}$ 
    80  M_theta       = $\theta_M$ 
    81  M_phi         = $\phi_M$ 
    82  Up_frac_i     = (spin up)/(spin up + spin down) neutrons *before* the sample 
    83  Up_frac_f     = (spin up)/(spin up + spin down) neutrons *after* the sample 
     91 M0:sld      $D_M M_0$ 
     92 mtheta:sld   $\theta_M$ 
     93 mphi:sld     $\phi_M$ 
     94 up:angle     $\theta_\mathrm{up}$ 
     95 up:frac_i    $u_i$ = (spin up)/(spin up + spin down) *before* the sample 
     96 up:frac_f    $u_f$ = (spin up)/(spin up + spin down) *after* the sample 
    8497===========   ================================================================ 
    8598 
    8699.. note:: 
    87     The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1. 
     100    The values of the 'up:frac_i' and 'up:frac_f' must be in the range 0 to 1. 
    88101 
    89102*Document History* 
    90103 
    91104| 2015-05-02 Steve King 
    92 | 2017-05-08 Paul Kienzle 
     105| 2017-11-15 Paul Kienzle 

  • doc/guide/pd/polydispersity.rst

    r75e4319 ra66b004  
    66.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    77 
     8.. _polydispersityhelp: 
     9 
    810Polydispersity Distributions 
    911---------------------------- 
    1012 
    11 With some models in sasmodels we can calculate the average form factor for a 
     13With some models in sasmodels we can calculate the average intensity for a 
    1214population of particles that exhibit size and/or orientational 
    13 polydispersity. The resultant form factor is normalized by the average 
     15polydispersity. The resultant intensity is normalized by the average 
    1416particle volume such that 
    1517 

  • doc/guide/resolution.rst

    r1f058ea r0db85af  
    209209$x'_0 = x_0 \cos(\theta) + y_0 \sin(\theta)$ and 
    210210$y'_0 = -x_0 \sin(\theta) + y_0 \cos(\theta)$. 
    211 Note that the rotation angle is zero for a $x$\ -\ $y$ symmetric 
     211Note that the rotation angle is zero for a $x$-$y$ symmetric 
    212212elliptical Gaussian distribution. The $A$ is a normalization factor. 
    213213 
    … …  
    233233 
    234234Since the weighting factor on each of the bins is known, it is convenient to 
    235 transform $x'$\ -\ $y'$ back to $x$\ -\ $y$ coordinates (by rotating it 
     235transform $x'$-$y'$ back to $x$-$y$ coordinates (by rotating it 
    236236by $-\theta$ around the $z$\ -axis). 
    237237 
    … …  
    254254    y'_0 &= 0 
    255255 
    256 while for a $x$\ -\ $y$ symmetric smear 
     256while for a $x$-$y$ symmetric smear 
    257257 
    258258.. math:: 
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